Method for converting solar energy

ABSTRACT

The present invention discloses a method for converting solar energy, comprises the following step of: providing a photovoltaic panel comprising a plurality of photovoltaic cells for gathering solar energy and converting the incident solar energy into electric energy; providing a multi-layer assembly comprising N layers, each layer adapted to contain a fluid stream; distributing the fluid streams to be heated into the N layers; rising temperature of the fluid streams within each layer of the multi-layer assembly by the heating of the multi-layer assembly and the photovoltaic panel; and collecting the heated fluid stream from the N layers; wherein N is a positive integer.

CROSS-REFERENCE TO RELATED APPLICATION

This is a Divisional application of U.S. application Ser. No. 12/905,349 filed Dec. 14, 2012, which is incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention is related to a method for converting solar energy. More particularly, the invention is related to the method for generating electric energy and heated fluid.

2. Description of the Prior Art

In general, traditional solar panels may have photovoltaic arrays placed on a flat plate for converting solar energy to electric energy, a series of tubes are secured to the flat plate for collecting solar radiation onto to the flat plate and the photovoltaic arrays, and water to be heated is circulated through these tubes to extract the heat received by the photovoltaic arrays and the flat plate. Furthermore, the water circulated through these tubes may be used as a coolant for taking away the heat generated by the photovoltaic arrays.

For example, U.S. Pat. No. 5,522,944 describes a multi-purpose solar energy conversion system for converting solar energy to thermal and electrical energy, said system includes an array of photovoltaic cells for converting solar energy to electrical energy, and a plurality of interconnected heat collecting tubes disposed on the same plane as the array of photovoltaic cells for converting solar energy to thermal energy in a fluid disposed within the heat collecting tubes. However, the system employs the tubes/pipes which are complicated to fabricate and failed to provide a fast and efficient way to assemble the entire system.

Besides, the system also suffers from cold and icy conditions, where the temperature is such that circulating water in the panel may freeze and burst the pipes. Thus, the complicated tubes/pipes shall be a problem for maintaining such system. There is therefore an unresolved need in the art for a simple, reliable and inexpensive system without complicated tubes/pipes for converting solar energy to thermal and electric energy.

SUMMARY OF THE INVENTION

A purpose of the present invention is to provide a simple, reliable and inexpensive solar energy converting method and a corresponding solar energy converter without complicated tubes/pipes for generating electric energy and heated fluid.

In accordance with the embodiment, the solar energy converter for generating electric energy and heated fluid comprises a multi-layer assembly, a photovoltaic panel and a manifold assembly. The multi-layer assembly is a casing and comprises N layers separated by at least one separator floor, each layer has at least one channel adapted to contain a fluid stream, and each layer has a first opening and a second opening. The photovoltaic panel has a top surface and a bottom surface, the bottom surface of the photovoltaic panel contacts the multi-layer assembly, the photovoltaic panel comprises a plurality of photovoltaic cells, disposed on the top surface, for gathering solar energy and converting the incident solar energy into electric energy, whereby the heating of the multi-layer assembly and the photovoltaic panel rises temperature of the fluid streams within each layer of the multi-layer assembly. The manifold assembly, detachably engaged with the multi-layer assembly, comprises N passages for containing the fluid streams, the Kth passage is adapted to distribute the fluid stream to be heated into the channel of the Kth layer through the corresponding first opening and collect the heated fluid stream from the channel of the Kth layer through the corresponding second opening, wherein N is a positive integer, K is a positive integer less than or equal to N.

In addition, the manifold assembly can be physically separated into a first manifold unit and a second manifold unit, the first manifold unit has N first passages, each of the first passages is adapted to align with the corresponding first opening of the multi-layer assembly, the second manifold unit has N second passages, each of the second passages is adapted to align with the corresponding second opening of the multi-layer assembly. Besides, each of the first passages of the first manifold unit comprises a first chamber and a first valve, the first chamber receives the fluid stream from a fluid source, and the first valve is adapted to align with the first opening of the channel of the corresponding layer for distributing the fluid stream to be heated into the channel of the corresponding layer. Moreover, the first chamber is a tubular space penetrating the first manifold unit and sealed by two end blocks at both ends, and at least one of the end blocks has an aperture thereon adapted to be detachably engaged with a connector for transporting the fluid stream from the fluid source to the first chamber.

A purpose of the present invention is to provide method for generating electric energy and heated fluid. Said method comprises the following steps: providing a photovoltaic panel comprising a plurality of photovoltaic cells for gathering solar energy and converting the incident solar energy into electric energy; providing a multi-layer assembly comprising N layers, each layer adapted to contain a fluid stream; distributing the fluid streams to be heated into the N layers; rising temperature of the fluid streams within each layer of the multi-layer assembly by the heating of the multi-layer assembly and the photovoltaic panel; collecting the heated fluid stream from the N layers, wherein N is a positive integer.

A purpose of the present invention is to provide a simple, reliable and inexpensive solar energy conversion system without complicated tubes/pipes for generating electric energy and heated fluid.

In accordance with the embodiment, the solar energy conversion system comprises a mounting frame, a plurality of solar energy converters, an umbilical connecting device. The plurality of solar energy converters are detachably fixed on the mounting frame respectively.

Each of the solar energy converter comprises a multi-layer assembly, a photovoltaic panel and a manifold assembly. The multi-layer assembly is a casing and comprises N layers separated by at least one separator floor, each layer has at least one channel adapted to contain a fluid stream, and each layer has a first opening and a second opening. The photovoltaic panel has a top surface and a bottom surface, the bottom surface of the photovoltaic panel contacts the multi-layer assembly, the photovoltaic panel comprises a plurality of photovoltaic cells, disposed on the top surface, for gathering solar energy and converting the incident solar energy into electric energy, whereby the heating of the multi-layer assembly and the photovoltaic panel rises temperature of the fluid streams within each layer of the multi-layer assembly. The manifold assembly, detachably engaged with the multi-layer assembly, comprises N passages for containing the fluid streams, the Kth passage is adapted to distribute the fluid stream to be heated into the channel of the Kth layer through the corresponding first opening and collect the heated fluid stream from the channel of the Kth layer through the corresponding second opening, wherein N is a positive integer, K is a positive integer less than or equal to N.

Besides, the umbilical connecting device physically combines the passages of at least two the manifold assemblies of the plurality of solar energy converters for sharing the fluid streams contained therein.

Accordingly, the solar energy converter of the present invention eliminates the need to utilize assembled piping, such as copper piping, internally under the photovoltaic panel. The multi-layer assembly and the manifold assembly can be manufactured in one step respectively, and the solar energy conversion system provides a user to easily assemble multiple units of the system by mounting them on the frame to accommodate the user's needs.

The objective of the present invention will no doubt become obvious to those of ordinary skill in the art after reading the following detailed description of the preferred embodiment, which is illustrated in following figures and drawings.

BRIEF DESCRIPTION OF THE APPENDED DRAWINGS

FIG. 1 illustrates a 3D diagram of a solar energy converter according to an embodiment of the invention.

FIG. 2 a illustrates a 3D diagram of the first manifold unit according to an embodiment of the invention.

FIG. 2 b illustrates a 3D diagram of the first manifold unit according to another embodiment of the invention.

FIG. 2 c illustrates a 3D diagram of the first manifold unit according to the other embodiment of the invention.

FIG. 2 d illustrates a sectional drawing along direction Z in FIG. 2 c.

FIG. 3 a illustrates a lateral view of the end block and a part of the connector according to an embodiment of the invention.

FIG. 3 b illustrates a schematic diagram of the end block and a part of the connector according to another embodiment of the invention.

FIG. 4 illustrates a flow chart according to an embodiment of the method of the present invention.

FIG. 5 illustrates a 3D diagram of a solar energy conversion system according to an embodiment of the invention.

FIG. 6 illustrates a schematic diagram of an umbilical connecting device according to an embodiment of the invention.

FIG. 7 a illustrates a schematic diagram of a folded solar energy conversion system according to an embodiment of the invention.

FIG. 7 b illustrates a schematic diagram of the unfolded solar energy conversion system according to an embodiment of the invention.

FIG. 7 c illustrates a vertical view of FIG. 7 b.

FIG. 8 illustrates a schematic diagram of another folded solar energy conversion system according to an embodiment of the invention.

FIG. 9 illustrates a section view of a jagged multi-layer assembly according to an embodiment of the invention.

FIG. 10 illustrates a schematic diagram of an expansion feature according to an embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

Please refer to FIG. 1, FIG. 1 illustrates a 3D diagram of a solar energy converter according to an embodiment of the invention. As shown in FIG. 1, the solar energy converter 1 has a multi-layer assembly 10, a photovoltaic panel 12, a manifold assembly comprising a first manifold unit 14 a and a second manifold unit 14 b.

The multi-layer assembly 10 is a casing and comprises N layers separated by a plurality of separator floors, N is a positive integer. For example, the multi-layer assembly 10 has two layers, first layer 102 a and second layer 102 b, in this embodiment, and the two layers are separated by a separator floor 104. In practice, each of the N layers of the multi-layer assembly 10 shall be parallel to one another, and each layer has several channels adapted to contain a fluid stream. For example, the first layer 102 a may be adapted to contain water stream and the second layer 102 b may be adapted to contain air stream. The channels of all the layers form a pattern of honey-comb in a cross-sectional view along an extension direction of the channels. The channels can also be separated by the separator floor 104, that is, the separator floor 104 can be manufactured in certain pattern for creating the N-layer structure and the channels within each layer.

In addition, the multi-layer assembly 10 is made of aluminum and manufactured by an aluminum extrusion process. The material of the multi-layer assembly 10 is generally constructed of extruded high strength aluminum alloy to assure long life, more specifically, the material of the multi-layer assembly 10 shall preferably be 6061 or 6063 aluminum. It should be mentioned that the multi-layer assembly 10 can be, but not limited to, made of any suitable ductile metal or material. Those skilled in the art can replace aluminum with other appropriate materials. By using an extruded aluminum multi-layer assembly 10, costly individual tube assemblies and frames can be avoided. Moreover, the jointless design of the multi-layer assembly 10 can reduce fluid leakages of those layers and potential failure points.

Furthermore, the multi-layer assembly 10 can be coated with a surface coating for enhancing protection from corrosive atmospheres and absorption of the infra-red spectrum of the incident solar energy. In practice, the multi-layer assembly 10 can be coated with a hard black anodizing to attract maximum heat from the sun's rays and improve absorption of solar radiation. Those skilled in the art can understand that the surface coating can further be powder coating, anodizing or other methods or materials. These coatings may contain carbon nano materials to enhance coating lifetimes, enhance energy absorption and provide enhanced thermal transfer between the photovoltaic panel 12 and the multi-layer assembly 10. Besides, the surface coating can cover entire or partial exterior of the multi-layer assembly 10, and the multi-layer assembly 10 can be arranged with its blackened surface facing the sun and sloped at a suitable angle to optimize the solar energy collected. The backside of the multi-layer assembly 10 can be insulated by a layer of insulating material such as glass wool or plastic foam.

The photovoltaic panel 12 has a top surface and a bottom surface, the bottom surface of the photovoltaic panel 12 contacts the multi-layer assembly 10, the photovoltaic panel 12 comprises a plurality of photovoltaic cells, disposed on the top surface, for gathering solar energy and converting the incident solar energy into electric energy, whereby the heating of the multi-layer assembly 10 and the photovoltaic panel 12 rises temperature of the fluid streams within each layer of the multi-layer assembly 10. In practice, the photovoltaic panel 12 does not necessarily cover the entire top surface of the multi-layer assembly 10, and the plurality of photovoltaic cells can be bonded to the top surface randomly or in array. The photovoltaic panel 12 can be further covered by tempered glass (not shown in figures) coated with anti-reflective coatings to enhance light transmission.

The manifold assembly can be detachably engaged with the multi-layer assembly 10. In practice, the manifold assembly comprises two physically separated manifold units, the first manifold unit 14 a and the second manifold unit 14 b, for containing the fluid streams. The inner structures of the first manifold unit 14 a and the second manifold unit 14 b are substantially the same. The first manifold unit 14 a and the second manifold unit 14 b can also be manufactured by the extrusion process mentioned above.

Please refer to FIG. 1 and FIG. 2 a, FIG. 2 a illustrates a 3D diagram of the first manifold unit 14 a according to an embodiment of the invention. As shown in figures, the first manifold unit 14 a has two first passages, passage 140 and 142. In practice, the first passage 140 has two parts, a first chamber 140 a and a first valve 140 b respectively, the first chamber 140 a receives the fluid stream from a fluid source (not shown in figures), and the first valve 140 b is adapted to align with the first opening of the corresponding layer for distributing the fluid stream to be heated into the channel of the corresponding layer. For example, the first passage 140 contains water stream, the first chamber 140 a receives the water stream from a water tank or a water supply, and the first valve 140 b distributes the water stream into the first layer 102 a. Similarly, the first passage 142 contains air stream in the first chamber 142 a, and the first valve 142 b distributes the air stream into the second layer 102 b.

Specifically, the first chambers 140 a and 142 a are tubular spaces penetrating the first manifold unit 14 a. For example, the first chambers 140 a can be sealed by two end blocks 144 at both ends, and at least one of the end blocks 144 has an aperture thereon adapted to be detachably engaged with a connector 146 for transporting the water stream from the water supply to the first chamber 140 a. It should be noticed that the fluid stream can be infused into the first chamber without using the end block 144. Please refer to FIG. 2 a and FIG. 2 b, FIG. 2 b illustrates a 3D diagram of the first manifold unit 14 a according to another embodiment of the invention. As shown in FIG. 2 a and FIG. 2 b, the first manifold unit 14 a can further comprises one or several air intakes 142 c connected the first chamber 142 a for receiving air stream from outside. In this case, the air intake 142 c can be integrated with a filter screen to keep the impurities in air from getting inside the first chamber 142 a.

The manifold assembly also incorporates a specialized spray device enable an external self-cleaning feature in the design to remove foreign debris from the top surface of the photovoltaic panel 12 and the multi-layer assembly 10 which might cause shadowing on the photovoltaic cells and lead to under performance of the entire array.

Please refer to FIG. 2 c and FIG. 2 d, FIG. 2 c illustrates a 3D diagram of the first manifold unit 14 a according to the other embodiment of the invention. FIG. 2 d illustrates a sectional drawing along direction Z in FIG. 2 c. As shown in FIG. 2 c and FIG. 2 d, the first manifold unit 14 a comprises a cleaning passage 148 for cleaning the photovoltaic panel 12, the cleaning passage comprises a cleaning chamber 148 a and a cleaning valve 148 b, the cleaning valve 148 b is substantially align with the top surface of the photovoltaic panel 12, the cleaning chamber 148 a contain water for gushing out of the cleaning valve 148 b to clean the photovoltaic panel 12.

In general, an O-ring or similar device can be further disposed between the first manifold unit 14 and the multi-layer assembly 10 for sealing the fluid stream within the first passage and the channel of the corresponding layer.

Regards to details of the end block 144 and the connector 146, please refer to FIG. 3 a, FIG. 3 a illustrates a lateral view of the end block 144 and a part of the connector 146 according to an embodiment of the invention. As shown in FIG. 3, the end block 144 located at one end of the first manifold unit 14 a for sealing the first chambers 140 a, the end block 144 has an aperture thereon adapted to be detachably engaged with a connector 146. Specifically, the end block 144 can also comprises an O-ring 144 a to avoid fluid leakage while connecting the connector 146.

In addition, the connector 146 can comprises a vaned or finned intake tube inserted into the aperture of the end block 144 to create a turbulent flow in the fluid stream for increasing a heat transfer efficiency. Please refer to FIG. 3 b, FIG. 3 b illustrates a schematic diagram of the end block 144 and a part of the connector 146 according to another embodiment of the invention. The connector 146 comprises a bent intake tube converts a portion of the mechanical energy of the circulating fluid stream to generate a turbulent flow environment in the fluid stream to enhance heat transfer between the photovoltaic cells and the fluid stream, preventing sedimentation and making the unit self cleaning.

The solar energy converter 1 can be further realized via the method of the present invention. Please refer to FIG. 1 and FIG. 4, FIG. 4 illustrates a flow chart according to an embodiment of the method of the present invention. As shown in figures, in step S30, the photovoltaic panel 12 is provided for gathering solar energy and converting the incident solar energy into electric energy. In general, the solar energy converter 1 can separate the solar energy into three separate energy streams. The photovoltaic panel 12 comprises a plurality of photovoltaic cells placed on the sun facing surface of the photovoltaic panel 12 for converting the incident solar energy into electric energy. In step S32, a multi-layer assembly 10 is provided for contain fluid streams. In practice, the multi-layer assembly 10 comprising N layers, each layer adapted to contain a fluid stream.

In step S34, the first manifold unit 14 a distributes the fluid streams to be heated into the N layers of the multi-layer assembly 10. In step S36, the heating of the multi-layer assembly 10 and the photovoltaic panel 12 rises temperature of the fluid streams within each layer of the multi-layer assembly 10, that is, the fluid streams within each layer of the multi-layer assembly 10 taking away the heat generated by the photovoltaic panel 12 during the conversion of thermal-electric energy and the heat incident into the multi-layer assembly 10 directly. Moreover, the efficiency of the photovoltaic panel 12 can be increased by cooling and maintaining a constant temperature throughout the daily solar cycle and thus mitigating the heat induced efficiency losses characteristic of photovoltaic cells.

In step S38, the second manifold unit 14 b collects the heated fluid stream from the N layers. In practice, the second manifold unit 14 b can be connected to a heating, a radiator, a geyser, a water tank, or other appropriate device. The first manifold unit 14 a can be connected to a fluid source for receiving the fluid stream. The second manifold unit 14 b can also be connected to a suction pump to extract the air out of the corresponding layer. Hot air produced with the present invention can be used in agriculture for drying of fruits and vegetables.

The present invention also discloses a solar energy conversion system, please refer to FIG. 1 and FIG. 5. FIG. 5 illustrates a 3D diagram of a solar energy conversion system according to an embodiment of the invention. As shown in figures, the solar energy conversion system 4 comprises a plurality of solar energy converter 1, the details of the solar energy converter 1 are not repeated here. It should be noticed that the plurality of solar energy converters 1 can connect to each other by “T” rails 20 a and corresponding “T” slots 20 b. Those skilled in the art can replace the “T” rails 20 a and “T” slots 20 b with other similar apparatus, for example a convex portion and a corresponding concave portion suitable to fix the convex portion. Therefore, the size of the solar energy conversion system 4 can be easily enlarged by connecting the plurality of solar energy converters 1.

The solar energy conversion system 4 comprises a mounting frame 22 having a plurality of risers 222 detachably engaged with one another. The solar energy converter 1 can be detachably mounted on the adjacent riser 222 by the same apparatus of the “T” rails and the corresponding “T” slots. Therefore, the connection of the solar energy conversion system 4 is very simple and easy by using the risers with the “T” rails and the corresponding “T” slots, and every solar energy converters 1 within the solar energy conversion system 4 can be located, aligned, and tight down with the mounting frame 22 at the same time.

In addition, the mounting frame 22 further comprises a groove and the solar energy converter 1 comprises a pin, the pin can be affixed to the sides of the solar energy converter 1 to locate into corresponding groove in the sides of the mounting frame 22 and also which allows for the solar energy converter 1 to be quickly mounted into the mounting frame 22.

Besides, the riser 222 may incorporate a tunnel 222 a through the entire length of the riser 222. The tunnel 222 a creates a vortex aides with a downward pressure reaction of the trapped wind inside the tunnel 222 a. Therefore, the solar energy conversion system 4 can be disposed firmly on a roof or other windy place.

Please refer to FIG. 5 and FIG. 6. FIG. 6 illustrates a schematic diagram of an umbilical connecting device according to an embodiment of the invention. As shown in figures, the solar energy conversion system 4 further comprises an umbilical connecting device 24 physically combining the passages of at least two the manifold assemblies of the plurality of solar energy converters 1 for sharing the fluid streams contained therein. In practice, the umbilical connecting device 24 connects the second manifold unit 14 b of one solar energy converter 1 to the first manifold unit 14 a of another solar energy converter 1. Thus, the fluid streams from the fluid sources or similar devices can be shared within all solar energy converters 1. It should be noticed that the plurality of solar energy converter 1 can be connected not only in series connections but also in parallel connections, that is, those skilled in the art can realize that the umbilical connecting device 24 can connect the second manifold unit 14 b of one solar energy converter 1 to the plurality of first manifold units 14 a of corresponding solar energy converters 1.

Those skilled in the art can further realize that the solar energy conversion system 4 is not necessarily a plane system. For example, the solar energy conversion system 4 can be folded to a small package as shown in FIG. 7 a, FIG. 7 b, and FIG. 7 c. FIG. 7 a illustrates a schematic diagram of a folded solar energy conversion system 4 according to an embodiment of the invention. FIG. 7 a illustrates a schematic diagram of a folded solar energy conversion system 4 according to an embodiment of the invention. FIG. 7 b illustrates a schematic diagram of the unfolded solar energy conversion system 4 according to an embodiment of the invention. FIG. 7 c illustrates a vertical view of FIG. 7 b. As shown in figures, the solar energy conversion system 4 comprises, for example, four solar energy converters 1, the manifold assembly of the solar energy converters 1, the mounting frame and the umbilical connecting device can be integrated inside a column 50. Specifically, small rotatable manifold assemblies are connected to each solar energy converters 1 and stacked inside the column 50. The umbilical connecting device applied in this embodiment shall be flexible and shielded tubes and cables. The amount of the solar energy converter 1 can vary and is not restricted to a particular number.

FIG. 8 illustrates a schematic diagram of another folded solar energy conversion system 4 according to an embodiment of the invention. The solar energy conversion system 4 in this embodiment comprises several solar energy converters 1, and the adjacent solar energy converters 1 can double up and connect to each other by the flexible umbilical connecting device 24.

FIG. 9 illustrates a section view of a jagged multi-layer assembly according to an embodiment of the invention. As shown in FIG. 9, the channels of all the layers form a jagged pattern in a cross-sectional view along an extension direction of the channels. The multi-layer assembly 10 and the photovoltaic panel 12 can be detachably engaged with each other. Of course, the photovoltaic panel 12 can be the upper cover of the multi-layer assembly 10, that is, the multi-layer assembly 10 can only comprise a casing without the upper cover, and the layers within the multi-layer assembly 10 can be separated jagged separator floors. Further, the multi-layer assembly 10 and the photovoltaic panel 12 can be roll welded on the edges.

FIG. 10 illustrates a schematic diagram of an expansion feature according to an embodiment of the invention. As shown in FIG. 10, the solar energy converter 1 of the solar energy conversion system 4 can be detachably engaged with a buffer block 60, and springs 62 can be placed between the buffer block 60 and the mounting frame 22 and create an expansion gap 64, the expansion feature of the present invention can absorb the temperature changes of the material and have the ability to expand and extract.

To sum up, the present invention is to provide the solar energy converter eliminates the need to utilize assembled piping, such as copper piping, internally under the photovoltaic panel. The multi-layer assembly and the manifold assembly can be manufactured in one step respectively, and the solar energy conversion system provides a user to easily assemble multiple units of the system by mounting them on the mounting frame to accommodate the user's needs.

With the example and explanations above, the features and spirits of the invention will be hopefully well described. Those skilled in the art will readily observe that numerous modifications and alterations of the device may be made while retaining the teaching of the invention. Accordingly, the above disclosure should be construed as limited only by the metes and bounds of the appended claims. 

What is claimed is:
 1. A method for generating electric energy and heated fluid, said method comprising the following steps: providing a photovoltaic panel comprising a plurality of photovoltaic cells for gathering solar energy and converting the incident solar energy into electric energy; providing a multi-layer assembly comprising N layers, each layer adapted to contain a fluid stream; distributing the fluid streams to be heated into the N layers; rising temperature of the fluid streams within each layer of the multi-layer assembly by the heating of the multi-layer assembly and the photovoltaic panel; and collecting the heated fluid stream from the N layers; wherein N is a positive integer.
 2. The method of claim 1, wherein the fluid streams within the N layers comprise at least two types of fluid.
 3. The method of claim 1, wherein the multi-layer assembly is made manufactured by an extrusion process.
 4. The method of claim 1, wherein the multi-layer assembly is coated with a surface coating for enhancing protection from corrosive atmospheres and absorption of the infra-red spectrum of the incident solar energy.
 5. The method of claim 1, wherein each layer of the multi-layer assembly comprises the plurality of channels, the channels of all the layers form a pattern of honey-comb in a cross-sectional view along an extension direction of the channels.
 6. The method of claim 1, further comprising the following step: receiving the fluid stream from a fluid source.
 7. The method of claim 1, further comprising the following step: generating a turbulent flow in the each fluid stream for increasing a heat transfer efficiency of the corresponding fluid stream. 